牛顿科茨公式计算超奇异积分的误差估计

超奇异积分的数值计算是边界元方法中的重要的课题之一,本文得到了牛顿科茨公式计算任意阶超奇异积分误差估计,当误筹函数中的Sκ(p)(Τ)=0时,便得到超收敛现象,并给出了Sκ(p)(Τ)之间的相互关系.相应的数值算例验证了理论分析的正确性.     

三步五阶迭代方法解非线性方程组

本文根据求积公式, 给出了三种求解非线性方程组的迭代方法, 并证明了所提出的三步迭代方法具有五阶收敛性. 最后给出了四个数值实例, 将本文的实验结果与现有的几种迭代方法的实验结果作了比较分析, 表明本文所提出的方法具有明显的优越性.     

A family of the Cauchy type mean-value theorems

The Cauchy type mean-value theorems for the Riemann-Liouville fractional derivative are deduced here from known mean-value theorems of the Lagrange type. A general method for deducing these Cauchy type formulas is extracted. Two Cauchy type formulas are then deduced without a priori knowledge about the Lagrange type mean-value theorems.     

On computing uniformly valid approximations for viscous waves on a plane beach

Existing expansions for the near- and far-field flow of linear waves in a viscous liquid on a plane beach are supplemented by an approximation in the intermediate region which enables the flow to be matched from the shore line to infinity. Methods of computation are discussed and incorporated are recent improvements on the performance of numerical computation of oscillatory integrals. Sidi's user-friendly W-transform (1988) and Köhler's parameter optimisation (this journal, 1993) for generalised Newton—Cotes quadrature are found to be significant elements particularly with regard to the inversion of the Kontorovich—Lebedev transform. Comprehensive computations are undertaken and diagrams shown to display the behaviour of the stream function for all depths. An attempt is also made to construct a composite expansion of the vorticity and this is computed on a ray bisecting the wedge.     

Generating functions for newton-cotes formulae weights and error terms

From the observation that weights in the Newton-Cotes formulae look like integrals of binomial coefficient polynomials, we are able to evaluate their generating function. We also obtain a generating function for the error terms in the Newton-Cotes formulae by generalizing the Euler-Maclaurin sum formula.     

关于《数值分析》教材中一道习题的商榷

指出研究生教材<数值分析>中习题的一处疏忽性错误,并给出几种可供参考的解法和必要的讨论.